During relativistic magnetic reconnection, antiparallel magnetic fields undergo a rapid change in topology, releasing a large amount of energy in the form of non-thermal particle acceleration. This work explores the application of mesh refinement to 2D reconnection simulations to efficiently model the inherent disparity in length-scales. We have systematically investigated the effects of mesh refinement and determined necessary modifications to the algorithm required to mitigate non-physical artifacts at the coarse–fine interface. We have used the ultrahigh-order pseudo-spectral analytical time-domain Maxwell solver to analyze how its use can mitigate the numerical dispersion that occurs with the finite-difference time-domain (or “Yee”) method. Absorbing layers are introduced at the coarse–fine interface to eliminate spurious effects that occur with mesh refinement. We also study how damping the electromagnetic fields and current density in the absorbing layer can help prevent the non-physical accumulation of charge and current density at the coarse–fine interface. Using a mesh refinement ratio of 8 for two-dimensional magnetic reconnection simulations, we obtained good agreement with the high-resolution baseline simulation, using only 36% of the macroparticles and 71% of the node-hours needed for the baseline. The methods presented here are especially applicable to 3D systems where higher memory savings are expected than in 2D, enabling comprehensive, computationally efficient 3D reconnection studies in the future.

Relativistic magnetic reconnection is a nonideal plasma process that is a source of nonthermal particle acceleration in many high-energy astrophysical systems. Particle-in-cell (PIC) methods are commonly used for simulating reconnection from first principles. While much progress has been made in understanding the physics of reconnection, especially in 2D, the adoption of advanced algorithms and numerical techniques for efficiently modeling such systems has been limited. With the GPU-accelerated PIC code WarpX, we explore the accuracy and potential performance benefits of two advanced Maxwell solver algorithms: a nonstandard finite-difference scheme (CKC) and an ultrahigh-order pseudo-spectral method (PSATD). We find that, for the relativistic reconnection problem, CKC and PSATD qualitatively and quantitatively match the standard Yee-grid finite-difference method. CKC and PSATD both admit a time step that is 40% longer than that of Yee, resulting in a ∼40% faster time to solution for CKC, but no performance benefit for PSATD when using a current deposition scheme that satisfies Gauss’s law. Relaxing this constraint maintains accuracy and yields a 30% speedup. Unlike Yee and CKC, PSATD is numerically stable at any time step, allowing for a larger time step than with the finite-difference methods. We found that increasing the time step 2.4–3 times over the standard Yee step still yields accurate results, but it only translates to modest performance improvements over CKC, due to the current deposition scheme used with PSATD. Further optimization of this scheme will likely improve the effective performance of PSATD.

We study the linear stability of a planar interface separating two fluids in relative motion, focusing on the symmetric configuration where the two fluids have the same properties (density, temperature, magnetic field strength, and direction). We consider the most general case with arbitrary sound speed c(s), Alfven speed v(A), and magnetic field orientation. For the instability associated with the fast mode, we find that the lower bound of unstable shear velocities is set by the requirement that the projection of the velocity on to the fluid-frame wavevector is larger than the projection of the Alfven speed on to the same direction, i.e. shear should overcome the effect of magnetic tension. In the frame where the two fluids move in opposite directions with equal speed v, the upper bound of unstable velocities corresponds to an effective relativistic Mach number M-re equivalent to v/v(f perpendicular to) root(1 - v(f perpendicular to)(2))/(1 - v(2))cos theta = root 2, where v(f perpendicular to) = [v(A)(2)+c(s)(2)(1-v(A)(2))](1/2) is the fast speed assuming a magnetic field perpendicular to the wavevector (here, all velocities are in units of the speed of light), and theta is the laboratory-frame angle between the flow velocity and the wavevector projection on to the shear interface. Our results have implications for shear flows in the magnetospheres of neutron stars and black holes both for single objects and for merging binaries where the Alfven speed may approach the speed of light.

We study the linear stability of a planar interface separating two fluids in relative motion, focusing on conditions appropriate for the boundaries of relativistic jets. The jet is magnetically dominated, whereas the ambient wind is gas-pressure-dominated. We derive the most general form of the dispersion relation and provide an analytical approximation of its solution for an ambient sound speed much smaller than the jet Alfven speed nu(A), as appropriate for realistic systems. The stability properties are chiefly determined by the angle psi between the wavevector and the jet magnetic field. For psi = pi/2, magnetic tension plays no role, and our solution resembles the one of a gas-pressure-dominated jet. Here, only sub-Alfvenic jets are unstable (0 < M-e equivalent to (nu/nu A) cos theta q < 1, where v is the shear velocity and theta the angle between the velocity and the wavevector). For psi = 0, the free energy in the velocity shear needs to overcome the magnetic tension, and only super-Alfvenic jets are unstable (1 < Me < root (1 + Gamma(2)(w))/[1 + (nu(A)/c)(2) Gamma(2)(w)], with Gamma(w) the wind adiabatic index). Our results have important implications for the propagation and emission of relativistic magnetized jets.

We revisit the question of whether the observed periodicity of comet impacts on Earth is consistent with Solar oscillation about the Galactic midplane and spiral arm crossings, here in the context of dissipative dark matter models. Consider whether a hypothetical thin dark disk, a signature of these models, is necessary to give the right periodicity, and whether such a dark disk is allowed given kinematic and other observational constraints on the Galaxy's gravitational potential, taking into account recent updates of these limits based on the vertical epicyclic oscillations of the tracer populations. Our analysis contains updated parameters for the Galactic disk, a self-consistent gravitational potential under the Poisson-Jeans equations, and includes prior probabilities from local stellar kinematics and the distribution of Milky Way interstellar gas. Moreover, our analysis also includes radial oscillations and Galactic spiral arm crossings. We find a dark disk explanation for the comet periodicity to be 10 times more likely than a constant average rate model. Moreover, we find that spiral arm crossing is necessary to correctly predict the date of the Chicxulub crater dated to 66 My ago.

Particle energization in shear flows is invoked to explain nonthermal emission from the boundaries of relativistic astrophysical jets. Yet the physics of particle injection, i.e., the mechanism that allows thermal particles to participate in shear-driven acceleration, remains unknown. With particle-in-cell simulations, we study the development of Kelvin-Helmholtz (KH) instabilities seeded by the velocity shear between a relativistic magnetically dominated electron-positron jet and a weakly magnetized electron-ion ambient plasma. We show that, in their nonlinear stages, KH vortices generate kinetic-scale reconnection layers, which efficiently energize the jet particles, thus providing a first-principles mechanism for particle injection into shear-driven acceleration. Our work lends support to spine-sheath models of jet emission-with a fast core/spine surrounded by a slower sheath-and can explain the origin of radio-emitting electrons at the boundaries of relativistic jets.

Scientific machine learning (SciML) promises to have a transformational impact on scientific exploration, by combining state-of-the-art AI methods with the latest generation of supercomputers. However, to efficiently leverage ML techniques on high-performance computing (HPC) systems, it is critical to understand the performance characteristics of the underlying algorithms on modern computational systems. In this work, we present a new methodology for developing a detailed performance understanding of ML benchmarks. To demonstrate our approach we investigate two emerging SciML benchmark applications from cosmology and climate, ComsoFlow and DeepCAM, as well as ResNet-50, a well-known image classification model. We develop and validate performance models that explore the key architectural artifacts, including memory requirements, data reuse, and performance efficiency across both single- and multiple-GPU computations. Our methodology also focuses on the complexity of data-movement across storage and memory hierarchies, and leverages our performance models to capture key components of runtime execution while highlighting design tradeoffs. Although our work focuses on image-processing methods on GPU-based HPC systems, our approach is applicable to a variety of ML algorithmic domains and emerging AI accelerators. Overall, our insights will help computer architects and data scientists understand performance bottlenecks and optimization opportunities to improve SciML design and system efficiency.

Maintaining computational load balance is important to the performant behavior of codes which operate under a distributed computing model. This is especially true for GPU architectures, which can suffer from memory oversubscription if improperly load balanced. We present enhancements to traditional load balancing approaches and explicitly target GPU architectures, exploring the resulting performance. A key component of our enhancements is the introduction of several GPU-amenable strategies for assessing compute work. These strategies are implemented and benchmarked to find the most optimal data collection methodology for in-situ assessment of GPU compute work. For the fully kinetic particle-in-cell code WarpX, which supports MPI+CUDA parallelism, we investigate the performance of the improved dynamic load balancing via a strong scaling-based performance model and show that, for a laserion acceleration test problem run with up to 6144 GPUs on Summit, the enhanced dynamic load balancing achieves from 62%-74% (88% when running on 6 GPUs) of the theoretically predicted maximum speedup; for the 96-GPU case, we find that dynamic load balancing improves performance relative to baselines without load balancing (3.8x speedup) and with static load balancing (1.2x speedup). Our results provide important insights into dynamic load balancing and performance assessment, and are particularly relevant in the context of distributed memory applications ran on GPUs.

The plasma in low-luminosity accretion flows, such as the one around the black hole at the center of M87 or Sgr A* at our Galactic Center, is expected to be collisioness and of two temperatures, with protons hotter than electrons. Here, particle heating is expected to be controlled by magnetic reconnection in the transrelativistic regime sigma(w) similar to 0.1-1, where the magnetization sigma(w) is the ratio of magnetic energy density to plasma enthalpy density. Using large-scale 2D particle-in-cell simulations, we explore for a fiducial sigma(w) = 0.1 how the dissipated magnetic energy is partitioned between electrons and protons as a function of beta(i) (the ratio of proton thermal pressure to magnetic pressure) and of the strength of a guide field B-g perpendicular to the reversing field B-0. At low beta(i) (less than or similar to 0.1), we find that the fraction of initial magnetic energy per particle converted into electron irreversible heat is nearly independent of B-g/B-0, whereas protons are heated much less with increasing B-g/B-0. As a result, for large B-g/B-0, electrons receive the overwhelming majority of irreversible particle heating (similar to 93% for B-g/B-0 = 6). This is significantly different than the antiparallel case B-g/B-0 = 0, in which irreversible electron heating accounts for only similar to 18% of the total particle heating (Rowan et al. 2017). At beta(i) similar to 2, when both species start already relativistically hot (for our fiducial sigma(w) = 0.1), electrons and protons each receive similar to 50% of the irreversible particle heating, regardless of the guide field strength. Our results provide important insights into the plasma physics of electron and proton heating in hot accretion flows around supermassive black holes.

The accretion flow around the Galactic Centre black hole Sagittarius A* (Sgr A*) is expected to have an electron temperature that is distinct from the ion temperature, due to weak Coulomb coupling in the low-density plasma. We present four two-temperature general relativistic radiative magnetohydrodynamic (GRRMHD) simulations of Sgr A* performed with the code KORAL. These simulations use different electron heating prescriptions, motivated by different models of the underlying plasma microphysics. We compare the Landau-damped turbulent cascade model used in a previous work with a new prescription we introduce based on the results of particle-in-cell simulations of magnetic reconnection. With the turbulent heating model, electrons are preferentially heated in the polar outflow, whereas with the reconnection model electrons are heated by nearly the same fraction everywhere in the accretion flow. The spectra of the two models are similar around the submillimetre synchrotron peak, but the models heated by magnetic reconnection produce variability more consistent with the level observed from Sgr A*. All models produce 230 GHz images with distinct black hole shadows which are consistent with the image size measured by the Event Horizon Telescope, but only the turbulent heating produces an anisotropic 'disc-jet' structure where the image is dominated by a polar outflow or jet at frequencies below the synchrotron peak. None of our models can reproduce the observed radio spectral slope, the large near-infrared and X-ray flares, or the near-infrared spectral index, all of which suggest non-thermal electrons are needed to fully explain the emission from Sgr A*.

Hot collisionless accretion flows, such as the one in Sgr A* at our Galactic center, provide a unique setting for the investigation of magnetic reconnection. Here protons are nonrelativistic, while electrons can be ultrarelativistic. By means of 2D particle-in-cell simulations, we investigate electron and proton heating in the outflows of transrelativistic reconnection (i.e., σ w ∼ 0.1 – 1 , where the magnetization σ w is the ratio of magnetic energy density to enthalpy density). For both electrons and protons, we find that heating at high β i (here β i is the ratio of proton thermal pressure to magnetic pressure) is dominated by adiabatic compression (“adiabatic heating”), while at low β i it is accompanied by a genuine increase in entropy (“irreversible heating”). For our fiducial σ w = 0.1 , the irreversible heating efficiency at β i ≲ 1 is nearly independent of the electron-to-proton temperature ratio T e / T i (which we vary from 0.1 up to 1), and it asymptotes to ∼ 2 % of the inflowing magnetic energy in the low- β i limit. Protons are heated more efficiently than electrons at low and moderate β i (by a factor of ∼7), whereas the electron and proton heating efficiencies become comparable at β i ∼ 2 if T e / T i = 1 , when both species start already relativistically hot. We find comparable heating efficiencies between the two species also in the limit of relativistic reconnection ( σ w ≳ 1 ). Our results have important implications for the two-temperature nature of collisionless accretion flows and may provide the subgrid physics needed in general relativistic MHD simulations.

We consider whether the observed periodicity of mass extinctions and of comet impacts on Earth is consistent with Solar oscillation about the Galactic midplane and spiral arm crossings. It is of further interest to determine whether a hypothetical thin dark disk is necessary to give the right periodicity, and whether such a dark disk is allowed given kinematic and other observational constaints on the Galaxyu0027s gravitational potential. We show that a dark disk consistent with recent bounds, combined with data for spiral arm crossing, can lead to the required periodicity. Moreover, we find that the best fit values correctly predict the date of the Chicxulub crater dated to 66 My ago.

This chapter demonstrates that simple mathematical methods can be used to design mazes that resemble user-supplied target images. The first approach discussed here is the TSP method, which involves converting the target image into a stipple drawing, and then treating the dots as the cities of a Traveling Salesman Problem (TSP). Another approach involves replacing the TSP with a much easier optimization problem—the problem of finding a minimum spanning tree (MST). The chapter then introduces a hybrid approach that produces mazes that have both the random textures of the original TSP Art and MST Art mazes and also the directional textures of the phyllotactic mazes. Finally, the chapter describes how to form a maze by constructing an image mosaic out of the vortex tiles.